We renormalize the Chern-Simons invariant for convex-cocompact hyperbolic 3-manifolds, finding the explicit asymptotics along an equidistance foliation. We prove that the divergent terms are completely expressed in terms of the data from the Weitzenböck geometry of hyperbolic ends and the conformal boundary. For this, it is essential to extend the framework of submanifolds in Riemannian geometry to Riemann-Cartan geometry, which addresses connections with torsion. This procedure naturally introduces a complex-valued geometric quantity consisting of mean curvature and torsion 2-form, which appears in the leading coefficient of the asymptotics. We also obtain several geometric results regarding the complex-valued quantity that generalize classical minimal surface theory.

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심사위원장: 백형렬, 심사위원: 박진성(KIAS), 김현규(KIAS), 박정환, 최서영.